## Abstract

A procedure for the selective extinction of the scattered light based on “null ellipsometry” [R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, 1977)] is presented. The technique allows scattering measurement from individual layers of a multilayer component by extinguishing the scattered light from the other layer interfaces. The technique is easily applicable to multilayer components with nearly identical surface profiles at every interface and little significant bulk scattering. Anal ysis is provided to determine the conditions required to extinguish the light from the excluded interfaces isolating the scattered light from the desired interface. An analysis of sensitivity of the extinction conditions to experimental parameters and to layer optical thickness is also provided. Experimental data collected using the technique are compared with measurements made using a white-light optical surface profilometry.

© 2011 Optical Society of America

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### Equations (22)

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(1)
$$\overrightarrow{A}(\theta ,\varphi )={A}_{s}(\theta ,\varphi )+{A}_{p}(\theta ,\varphi ),$$
(2)
$$f(\overrightarrow{A}(\theta ,\varphi ))=\mathrm{cos}\psi {A}_{s}(\theta ,\varphi )+\mathrm{sin}\psi {e}^{i\eta}{A}_{p}(\theta ,\varphi ),$$
(3)
$$f(\overrightarrow{A}(\theta ,\varphi ))=\mathrm{cos}\psi ({A}_{s}(\theta ,\varphi )+z{A}_{p}(\theta ,\varphi )),$$
(4)
$$z=\mathrm{tan}\psi {e}^{i\eta},$$
(5)
$$f(\overrightarrow{A}(\theta ,\varphi ))=0\iff z=\mathrm{tan}\psi (\theta ,\varphi ){e}^{i\eta (\theta ,\varphi )}=-\frac{{A}_{s}(\theta ,\varphi )}{{A}_{p}(\theta ,\varphi )}.$$
(6)
$$\psi (\theta ,\varphi )=\mathrm{arctan}\left|\frac{{A}_{s}(\theta ,\varphi )}{{A}_{p}(\theta ,\varphi )}\right|,\phantom{\rule[-0.0ex]{2.0em}{0.0ex}}\eta (\theta ,\varphi )=\pi +\mathrm{arg}\left(\frac{{A}_{s}(\theta ,\varphi )}{{A}_{p}(\theta ,\varphi )}\right).$$
(7)
$$\overrightarrow{A}(\theta ,\varphi )=\sum _{i}{\overrightarrow{A}}_{i}(\theta ,\varphi )+{\overrightarrow{A}}^{*}(\theta ,\varphi ).$$
(8)
$$f(\overrightarrow{A})=\mathrm{cos}\psi ({A}_{s}+z{A}_{p})=\mathrm{cos}\psi (\sum _{i}{\overrightarrow{A}}_{is}+{\overrightarrow{A}}_{s}^{*}+z(\sum _{i}{\overrightarrow{A}}_{ip}+{\overrightarrow{A}}_{p}^{*}\left)\right).$$
(9)
$${z}_{i\ne k}=-\frac{\sum _{i\ne k}{A}_{s}^{i}}{\sum _{i\ne k}{A}_{p}^{i}}.$$
(10)
$${A}_{uv}(\theta ,\varphi )=\sum _{i}{c}_{uv}^{i}(\theta ,\varphi ){g}^{i}(\theta ,\varphi ){A}_{u}.$$
(11)
$${g}^{i}(\theta ,\varphi )=g(\theta ,\varphi )\mathrm{.}$$
(12)
$${A}_{uv}(\theta ,\varphi )=g(\theta ,\varphi )\sum _{i}{c}_{uv}^{i}(\theta ,\varphi ){A}_{u}.$$
(13)
$$\psi =\mathrm{arctan}\left|\frac{\sum _{i}{c}_{s}^{i}(\theta ,\varphi )}{\sum _{i}{c}_{p}^{i}(\theta ,\varphi )}\right|,\phantom{\rule[-0.0ex]{2.0em}{0.0ex}}\eta =\pi +\mathrm{arg}\left(\frac{\sum _{i}{c}_{s}^{i}(\theta ,\varphi )}{\sum _{i}{c}_{p}^{i}(\theta ,\varphi )}\right).$$
(14)
$${A}_{uv}(\theta ,\varphi )={c}_{uv}^{0}(\theta ,\varphi )g(\theta ,\varphi ){A}_{u}+{c}_{uv}^{1}(\theta ,\varphi )g(\theta ,\varphi ){A}_{u}\mathrm{.}$$
(15)
$$\mathrm{cos}{\psi}_{0}({A}_{s}^{0}+{z}_{0}{A}_{p}^{0})=0.$$
(16)
$$f(\overrightarrow{A})=\mathrm{cos}{\psi}_{0}[({A}_{s}^{0}+{A}_{s}^{1})+{z}_{0}({A}_{p}^{0}+{A}_{p}^{1})]=\mathrm{cos}{\psi}_{0}[({A}_{s}^{0}+{z}_{0}{A}_{p}^{0})+({A}_{s}^{1}+{z}_{0}{A}_{p}^{1})]\mathrm{.}$$
(17)
$$f(\overrightarrow{A})=\mathrm{cos}{\psi}_{0}[{A}_{s}^{1}+{z}_{0}{A}_{p}^{1}]=f({z}_{0},{\overrightarrow{A}}_{1})\mathrm{.}$$
(18)
$$f(\overrightarrow{A})=\mathrm{cos}{\psi}_{0}({A}_{s}+{z}_{0}{A}_{p})\mathrm{.}$$
(19)
$$\gamma (\theta ,\varphi )=\frac{4{\pi}^{2}}{S}|g(\theta ,\varphi ){|}^{2},$$
(20)
$$f(\overrightarrow{A})=\mathrm{cos}{\psi}_{0}[{A}_{s}^{1}+{z}_{0}{A}_{p}^{1}]=\mathrm{cos}{\psi}_{0}[({c}_{s}^{1}{g}^{1}{A}_{s})+{z}_{0}({c}_{p}^{1}{g}^{1}{A}_{p})]={g}^{1}\mathrm{cos}{\psi}_{0}[({c}_{s}^{1}{A}_{s})+{z}_{0}({c}_{p}^{1}{A}_{p})],$$
(21)
$${A}_{s}={A}_{p}\mathrm{.}$$
(22)
$$f(\overrightarrow{A})={g}^{1}\mathrm{cos}{\psi}_{0}[{c}_{s}^{1}+{z}_{0}{c}_{p}^{1}]A={g}^{1}[{c}_{s}^{1\prime}+{c}_{p}^{1\prime}]A\mathrm{.}$$